Mathematical Experiment 4

Construct the envelope of the light rays emitted from a radiant point source at infinity after reflection by the semi-circle.

caustic1.mws

Construct the envelope of the light rays emitted from a radiant point source at the circumference after reflection by the same circle.

caustic2.mws
See also: spreadsheet worksheet
See also: Derive worksheet

Construct the envelope formed by a fix diameter of a circle rolling along a straight line.

diam-cyc.mws

Construct the envelope formed by a fix diameter of a circle rolling along a fixed circle of the same size.

diam-nep.mws

Construct the envelope formed by a fix diameter of a circle rolling along a fixed circle twice the diameter.

Construct this figure:

diam-6.mws

Construct this figure:

diam-8.mws

Construct this design:

design.mws

Construct the nested squares as thus:

nested-sq.mws

Constructed nested triangles as thus:

Construct this pattern:

pattern2.mws

Construct the family of ellipses

as t ranges in [0,1].

ast-ell.mws

Construct the concentric and coaxial ellipses of constant area:

Construct this pattern.

pattern.mws

Construct this pattern.

pattern.mws

Construct the reflections of a light ray trapped inside a reflective ellipse. There are two cases.

refl-ell.mws

refl-ell2.mws

restart;with(linalg):
> a:=5:b:=3:r:=1.34:s:=5.9;
> ll:=[a*cos(r),b*sin(r)]:l:=[a*cos(s),b*sin(s)];
> m:=[l,ll];
> for k to 200 do u:=ll-l: n:=[-b*ll[1]/a,-a*ll[2]/b]:v:=u-2*dotprod(u , n)*n/dotprod(n,n):t:=-2*(b^2*v[1]*ll[1]+a^2*ll[2]*v[2])/(b^2*v[1]^2 +a^2*v[2]^2):lll:=ll+t*v:m:=[op(m),lll]:l:=ll:ll:=lll:od:
> plot(m,scaling=constrained,axes=none);